Problem Solving

Set A consists of integers {3, -8, Y, 19, -6} and Set B consists of integers {K, -3, 0, 16, -5, 9}. Number L represents the median of Set A, number M represents the mode of set B, and number Z = LM. If Y is an integer greater than 21, for what value of K will Z be a divisor of 26?

A.-2
B.-1
C.0
D.1
E.2

If Y is an integer greater than 21, for what value of k will Z be a divisor of 26?
Median is the value at the center if set is odd and average of the two values at the center if set is even.
Given that Y> 21; Set A in ascending order will be $$\left(-8,-6,\ 3,\ 19,\ Y\right)$$
The median for set A will be 3 irrespective of the exact value of Y so L=3
$$Z=L^M=3^M$$
For Z to be divisor of 26, The values can be 1,2,13,26 but as 26 is not a power of 3, then M is either = 0 or some irrational numbers.
Since K is an integer, the M cannot be an irrational number as median of set B
so M=0
$$Z=3^M$$
$$Z=3^0$$
$$Z=1$$
M=0 , mode of set B
$$Set\ B\ in\ ascending\ order\ \left(-9,-3,\ 0,\ 9,\ 16,\ K\right)$$
All the integers appear once since mode is 0 elements of set B with highest frequency must be 0 hence k = 0
$$set\ B=\ \left(-5,3,\ 0,0,9,16\right)$$
$$Median\ =\frac{\left(0+0\right)}{2}=\frac{0}{2}=0$$
$$answer\ is\ Option\ C$$